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# Hypothesis Testing of Mean

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1. Last year, according to consumer group, the average passenger vehicle was driven 10.3 thousand miles with a standard deviation of 2 thousand miles before a claim of accident was made. A random sample of 225 passenger cars was collected by the auto insurance company which showed a mean of 10.1 thousand miles driven when a claim was made. Should the insurance company reject the consumer group's claim? A significance level of .05 was used. A manufacturer of vitamins claimed that its iron pills contain at least 18 mg of iron. A sample of 16 pills yield an average of 17.3 mg with a sample standard deviation of 1 mg. Should we reject the manufacturer's claim that the pills contain at least 18 mg of iron? We assume the population of iron content in all these pills is normally distributed and use a significance level of .01. You should follow the 10step procedure to perform this test.
a) Yes, we should reject the null hypothesis
b) No, we should not reject the null hypothesis

10 Step Procedure:

1. State H0 H0 = µ &#8805; 10.1 thousand miles
2. State H1 H1 = µ &#8804; 10.1 thousand miles
3. Choose &#945; &#945; = .05
4. Choose n n = 225
5. Choose Test Z Test (or p Value)
6. Set Up Critical Value(s) Z = ????????
7. Collect Data 225 passenger cars
8. Compute Test Statistic Computed Test Stat.= ???????
9. Make Statistical Decision ?????
10. Express Decision The true mean # of ???????????????

2. A manufacturer of vitamins claimed that its iron pills contain at least 18 mg of iron. A sample of 16 pills yield an average of 17.3 mg with a sample standard deviation of 1 mg. Should we reject the manufacturer's claim that the pills contain at least 18 mg of iron? We assume the population of iron content in all these pills is normally distributed and use a significance level of .01. You should follow the 10step procedure to perform this test.
a) Yes, we should reject the null hypothesis
b) No, we should not reject the null hypothesis

1. State H0 H0 = µ &#8805; 18 mg
2. State H1 H1 = µ &#8804; 18 mg
3. Choose &#945; &#945; = .01
4. Choose n n = ????
5. Choose Test Z Test (or p Value)
6. Set Up Critical Value(s) Z = ?????
7. Collect Data ???????
8. Compute Test Statistic Computed Test Stat.= ???????????
9. Make Statistical Decision ?????
10. Express Decision The true mean #

See attached problems for completion.

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#### Solution Summary

The solution provides step by step method for the calculation of testing of hypothesis. Formula for the calculation and Interpretations of the results are also included. Interactive excel sheet is included. The user can edit the inputs and obtain the complete results for a new set of data.

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## Franklin Park Mall Hypothesis Testing

The owners of the Franklin Park Mall wished to study customer shopping habits. From earlier
studies the owners are under the impression that a typical shopper spends 0.75 hours at the mall,
with a standard deviation of 0.10 hours. Recently the mall owners added some specialty restaurants designed to keep shoppers in the mall longer. The consulting firm, Brunner and Swanson Marketing Enterprises, has been hired to evaluate the effects of the restaurants. A sample of 45 shoppers by Brunner and Swanson revealed that the mean time spent in the mall had increased to 0.80 hours.
a. Develop a test of hypothesis to determine if the mean time spent in the mall is more than
0.75 hours. Use the .05 significance level.
b. Suppose the mean shopping time actually increased from 0.75 hours to 0.77 hours. What is
the probability this increase would not be detected?
c. When Brunner and Swanson reported the information in part (b) to the mall owners, the owners
were upset with the statement that a survey could not detect a change from 0.75 to 0.77
hours of shopping time. How could this probability be reduced?

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